If I move my Fiora Fearless into an empty battlefield and then my opponent plays Rengar Trophy Hunter, does my Fiora effect trigger to get double might?

Yes, Fiora, Peerless's ability will still trigger and her Might will be doubled.

According to RiftJudge FAQ #1231 and #11203, Fiora, Peerless's "When I attack or defend" ability is a triggered ability that checks the "one-on-one" condition only at the exact moment she is designated as the attacker or defender.

The Timing Sequence

1. Designation: You move Fiora, Peerless to an empty battlefield, initiating combat. Because she is the only unit there, the battlefield is "one-on-one" at that exact moment.
2. Trigger: Her triggered ability ("When I attack... double my Might") is placed on the Initial Chain.
3. Reaction: The game state is now Closed. Your opponent plays Rengar, Trophy Hunter using his [Ambush] keyword as a [Reaction].
4. Resolution: Rengar, Trophy Hunter enters the battlefield. Then, the Initial Chain resolves.

Because Fiora's ability uses "when" (a triggered ability) rather than "while" (a passive ability), it does not retroactively check the condition upon resolution. Since the "one-on-one" condition was satisfied at the moment she was designated as the attacker, the bonus is guaranteed once the trigger is on the chain. Adding Rengar to the battlefield afterwards does not negate the trigger.